Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations

Muhammad Zishan Anwar, Ahmad N. Al-Kenani, Shahida Bashir and Muhammad Shabir
Additional contact information
Muhammad Zishan Anwar: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Ahmad N. Al-Kenani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
Shahida Bashir: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Muhammad Shabir: Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan

Mathematics, 2022, vol. 10, issue 5, 1-23

Abstract: Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm.

Keywords: intuitionistic fuzzy set; soft relation; multigranulation roughness; decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/5/685/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/5/685/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:5:p:685-:d:756039

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().